practice(exam2)MA262fall2011

practice(exam2)MA262fall2011 - PRACTICE PROBLEMS FOR EXAM 2...

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PRACTICE PROBLEMS FOR EXAM 2 - MA 262 FALL 2011 INSTRUCTOR: RAPHAEL HORA 1. If A = 1 1 1 1 3 - 4 1 2 - 5 , then det( - 3 A ) =? (Hint: If A is an n x n matrix, then det( cA ) = c n det( A ), for any c R . ) 2. Compute ± ± ± ± ± ± 5 5 5 - 2 - 4 10 1 3 - 4 ± ± ± ± ± ± . 3. If A, B and C are 5 x 5 matrices such that det( A ) = 5, det( B ) = - 2 and det( C ) = - 4, then det( - AB - 1 C T )=? 4. Determine all values of k such that the vectors (1 , 1 , 1) , (2 ,k, 3) and ( - 1 , - 1 ,k - 2) are a basis for R 3 . (Hint: Find all values of k such that the determinant of the matrix whose rows are the given vectors is different from zero.) 5. Which of the following subsets S of the given vector space V is a subspace? (1) V = C 2 ( R ), S = { y 00 - (ln x + cos 3 x ) y 0 + (1 + e - 2 x sin x ) y = 0 } ; (2) V = P 3 , S = { x 3 + ax 2 + bx : a,b R } ; (3) V = R 3 , S = { ( x + 2 y,x - y, 0) : x,y R } ; (4) V = R 2 , S = { ( a,b ) : a 0 ,b R } ; (5) V = P 4 , S consists of all polynomials with degree 2 and the zero polynomial;
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This note was uploaded on 03/01/2012 for the course MA 262 taught by Professor Ber during the Fall '08 term at Purdue University-West Lafayette.

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practice(exam2)MA262fall2011 - PRACTICE PROBLEMS FOR EXAM 2...

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